False-name-proof combinatorial auction design via single-minded decomposition

This paper proposes a new approach to building false-name-proof (FNP) combinatorial auctions from those that are FNP only with single-minded bidders, each of whom requires only one particular bundle. Under this approach, a general bidder is decomposed into a set of single-minded bidders, and after the decomposition the price and the allocation are determined by the FNP auctions for single-minded bidders. We first show that the auctions we get with the single-minded decomposition are FNP if those for single-minded bidders satisfy a condition called PIA. We then show that another condition, weaker than PIA, is necessary for the decomposition to build FNP auctions. To close the gap between the two conditions, we have found another sufficient condition weaker than PIA for the decomposition to produce strategy-proof mechanisms. Furthermore, we demonstrate that once we have PIA, the mechanisms created by the decomposition actually satisfy a stronger version of false-name-proofness, called false-name-proofness with withdrawal

A Complexity Approach for Core-Selecting Exchange under Conditionally Lexicographic Preferences

International audienceCore-selection is a crucial property of rules in the literature of resource allocation. It is also desirable, from the perspective of mechanism design, to address the incentive of agents to cheat by misreporting their preferences. This paper investigates the exchange problem where (i) each agent is initially endowed with (possibly multiple) indivisible goods, (ii) agents' preferences are assumed to be conditionally lexicographic, and (iii) side payments are prohibited. We propose an exchange rule called augmented top-trading-cycles (ATTC), based on the original TTC procedure. We first show that ATTC is core-selecting and runs in polynomial time with respect to the number of goods. We then show that finding a beneficial misreport under ATTC is NP-hard. We finally clarify relationship of misreporting with splitting and hiding, two different types of manipulations, under ATTC